Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Security of Quantum Key Distribution with Weak Coherent Pulses

駿 川上

Published Mar 23, 2017• 1 citation
Publisher

Abstract

Quantum key distribution (QKD) allows two distant parties to share a secret key and realizes a communication with information-theoretic security by combining it with one-time-pad encryption.Since the Bennett-Brassard 1984 (BB84) protocol was proposed, a large number of researches on QKD have been conducted from both aspects of theory and implementations.For implementations of QKD, weak coherent pulses (WCP) are heavily used as optical signals because they are easily generated by typical lasers and attenuators.The security for QKD with WCP has been also studied along the development of the implementations.In this thesis, the security analysis of the QKD with WCP is considered and further developed from two aspects.First, the security of the differential-quadrature-phase-shift (DQPS) protocol is proved.The DQPS protocol has essentially the same set up as the phase-encoding BB84 (PE-BB84) protocol, which is one of the most frequently demonstrated protocols.Since the known proof techniques for the BB84 protocol is not directly applicable, a modified approach is developed which is suitable for the DQPS protocol.As a result, the advantage of the DQPS protocol in the key generation rate over the PE-BB84 protocol is shown in the asymptotic limit where the size of communication data is assumed to be infinite.Second, a new method for security analysis with finite-key size is proposed as a suitable method for QKD protocols using WCP.Differently from the current method based on simple random sampling, the proposed method relies on Bernoulli sampling, which is associated with binomial distribution.The security of the BB84 protocol is proved by using the Bernoulli-sampling method, enabling a simpler analysis with a smaller number of parameters to be estimated compared to the method with simple random sampling.The required number of detected signals to generate a secret key is shown to be smaller than 10 4 , which is drastic improvement from the number ∼ 10 7 obtained in the previous result.The proposed method is also applied to the DQPS protocol, and its advantage over the PE-BB84 protocol is certified even in the finite-key regime.i

DOI
10.15083/00075742

Related papers

Finite-key analysis for quantum key distribution with weak coherent pulses based on Bernoulli sampling

Shun Kawakami, Toshihiko Sasaki, Masato Koashi

An essential step in quantum key distribution is the estimation of parameters related to the leaked amount of information, which is usually done by sampling of the communication data. When the data size is finite, the final key rate depends on how the estimation process handles statistical fluctuations. Many of the present security analyses are based on the method with simple random sampling, where hypergeometric distribution or its known bounds are used for the estimation. Here we propose a concise method based on Bernoulli sampling, which is related to binomial distribution. Our method is suitable for the Bennett-Brassard 1984 (BB84) protocol with weak coherent pulses [C. H. Bennett and G. Brassard, Proceedings of the IEEE Conference on Computers, Systems and Signal Processing (IEEE, New York, 1984), Vol. 175], reducing the number of estimated parameters to achieve a higher key generation rate compared to the method with simple random sampling. We also apply the method to prove the security of the differential-quadrature-phase-shift (DQPS) protocol in the finite-key regime. The result indicates that the advantage of the DQPS protocol over the phase-encoding BB84 protocol in terms of the key rate, which was previously confirmed in the asymptotic regime, persists in the finite-key regime.

arXiv:1701.04168•Physical Review A•Jul 5, 2017•4 citations

Security of the differential-quadrature-phase-shift quantum key distribution

Shun Kawakami, Toshihiko Sasaki, Masato Koashi

One of the simplest methods for implementing quantum key distribution over fiber-optic communication is the Bennett-Brassard 1984 protocol with phase encoding (PE-BB84 protocol), in which the sender uses phase modulation over double pulses from a laser and the receiver uses a passive delayed interferometer. Using essentially the same setup and by regarding a train of many pulses as a single block, one can carry out the so-called differential-quadrature-phase-shift (DQPS) protocol, which is a variant of differential-phase-shift (DPS) protocols. Here we prove the security of the DQPS protocol based on an adaptation of proof techniques for the BB84 protocol, which inherits the advantages arising from the simplicity of the protocol, such as accommodating the use of threshold detectors and simple off-line calibration methods for the light source. We show that the secure key rate of the DQPS protocol in the proof is eight-thirds as high as the rate of the PE-BB84 protocol.

arXiv:1512.08129•Physical Review A•Aug 24, 2016•16 citations

Finite key analysis for discrete phase randomized BB84 protocol

Xiao-Hang Jin, Zhen−Qiang Yin, Shuang Wang +3 more

Abstract Quantum key distribution (QKD) is a secure communication method that relies on the inherent randomness of quantum mechanics to ensure information-theoretic security. The first and most widely used QKD protocol is BB84, and the proof of BB84's security is vital. The Discrete Phase Randomized BB84 protocol is a variant of the decoy BB84 protocol. It has been proven to be promising in the development of high-speed QKD systems. However, it still lacks an analysis with a finite number of pulses. This paper presents a comprehensive security analysis of the discrete phase BB84 protocol, using two different methods under different conditions. The analysis involves simulations and optimizations to determine the optimal parameter settings. It is confirmed that for typical scenarios, if the number of discrete phases exceeds 30, one can calculate the key rate by assuming that a continuous phase randomization process was in operation. On the other hand, for a relatively smaller number of discrete values, we have developed a numerical method to calculate the key rate. We have confirmed that its performance is reduced but still acceptable with a finite number of pulses.

Quantum Information Processing•Aug 31, 2024•2 citations

Optical key distribution enhanced by optical injection locking (Conference Presentation)

George L. Roberts, J. F. Dynes, Seb J. Savory +3 more

Quantum key distribution (QKD) allows two users to communicate with theoretically provable secrecy [1]. This is vitally important to secure the confidential data of governments, businesses and individuals. As the technology is adopted by a wider audience, a quantum network will become necessary for multi-party communication, as in the classical communication networks in use today. Unfortunately, a number of phase-encoded QKD protocols based on weak coherent pulses have been developed. Whilst the first protocol, proposed by Bennett and Brassard in 1984 (BB84), is still commonly used, other protocols such as differential phase shift [2] or coherent one way QKD [3] are also adopted. Each protocol has its benefits; however all would require a different transmitter and receiver, increasing the complexity and cost of quantum networks. In this work we demonstrate a multi-protocol transmitter [4-6] that also has the benefits of small footprint, low power consumption and low complexity. We use this transmitter to give the first experimental demonstration of an improved version of the BB84 protocol, known as the differential quadrature phase shift protocol. We have achieved megabit per second secure key rates at short distances, and have shown secure key rates that are, on average, 2.71 times higher than the standard BB84 protocol. This enhanced performance over such a commonly adopted protocol, at no expense to experimental complexity, could lead to a widespread migration to the new protocol. The security of the BB84 protocol relies on each signal and reference pulse pair being globally phase randomised with respect to all other pulse pairs. In the DQPS protocol, blocks with a length L ≥ 2 are used and each block has a globally random phase with respect to all other blocks. Implementing this protocol would ordinarily require a high-speed random number generator and a phase modulator. As well as increasing device complexity, it would also require an unrealistic continuous source of electrical modulation signals for complete security. The transmitter we use injects light from a master laser diode into a 2 GHz gain-switched slave laser diode. The principal of optical injection locking means that the slave laser inherits the phase of the master laser. We apply modulations to the master laser current within a block to control the phase of the slave laser output pulses, and then drive the master laser below threshold for a short period of time when phase randomisation is required. This ensures the lasing comes from below threshold, thus the phase adopted by the slave laser pulse is completely random. We perform an autocorrelation measurement on the blocks to show their randomness. [1] N. Gisin et al. Rev. Mod. Phys. 74, 145 (2002). [2] K. Inoue et al. Phys. Rev. Lett. 89, 037902 (2002). [3] D. Stucki et al. Appl. Phys. Lett. 87 194108 (2005). [4] Z. Yuan et al. Phys. Rev. X. 6, 031044 (2016). [5] G. L. Roberts et al. Laser Phot. Rev. 11, 1700067 (2017). [6] G. L. Roberts et al. arXiv:1709.04214 [quant-ph] (2017).

SPIE Quantum Technologies•May 29, 2018•0 citations

Finite-key security analysis of differential-phase-shift quantum key distribution

Akihiro Mizutani, Yuki Takeuchi, Kiyoshi Tamaki

Differential-phase-shift (DPS) quantum key distribution (QKD) is one of the major QKD protocols that can be implemented with a simple setup using a laser source and a passive detection unit. Recently, an information-theoretic security proof of this protocol was established by Mizutani et al. [npj Quantum Inf. 5, 87 (2019)], assuming an infinitely large number of emitted pulses. To implement the DPS protocol in a real-life world, it is indispensable to analyze the security with the finite number of emitted pulses. The extension of the security proof to the finite-size regime requires the accommodation of the statistical fluctuations to determine the amount of privacy amplification. In doing so, Azuma's inequality is often employed, but unfortunately we show that in the case of the DPS protocol, this results in a substantially low key rate. This low key rate is due to a loose estimation of the sum of probabilities regarding three-photon emission whose probability of occurrence is very small. The main contribution of our work is to show that this obstacle can be overcome by exploiting the recently found novel concentration inequality, Kato's inequality. As a result, the key rate of the DPS protocol is drastically improved. For instance, assuming typical experimental parameters, a 3-Mbit secret key can be generated over 77 km for 8.3 hours, which shows the feasibility of DPS QKD under a realistic setup.

arXiv:2301.09844•Physical Review Research•May 30, 2023•18 citations

Analysis of PNS Attacks on Quantum Key Distribution Protocols

Madhu Venkat Dasari, S. Kirubakaran, A. Paventhan

Quantum Key Distribution (QKD) is one of the most promising technologies that enable theoretically unbreakable secure communications in this highly advanced information security era. This work provides a comparative analysis of QKD protocols such as BB84, Coherent One-Way (COW), and Differential Phase-Shift (DPS) against eavesdropping attacks e.g., Photon Number Splitting (PNS) attack. It employs a realistic approach to simulations such as using weak coherent pulse (WCP) sources. This work also explores qubit generation and the whole key distribution process in non-ideal conditions. Detailed algorithms have been discussed that simulate the encoding, transmission, and decoding process for every protocol, as well as simulating PNS attacks where an eavesdropper removes photons to gain key information without any detectable errors. Statistical metrics, such as Visibility and the information gain, are used to quantify the impact of these attacks. Future work aspects may include the extension of the simulation to incorporate additional parameters such as channel noise, fiber attenuation, detector dark counts, etc. to provide a realistic analysis to compare various QKD protocols.

IEEE Wireless Antenna and Microwave Symposium (WAMS)•Jun 5, 2025•1 citation
Quantum key distribution (QKD) allows two distant parties to share a secret key and realizes a communication with information-theoretic security by combining it with one-time-pad encryption.Since the Bennett-Brassard 1984 (BB84) protocol was proposed, a large number of researches on QKD have been conducted from both aspects of theory and implementations.For implementations of QKD, weak coherent pulses (WCP) are heavily used as optical signals because they are easily generated by typical lasers and attenuators.The security for QKD with WCP has been also studied along the development of the implementations.In this thesis, the security analysis of the QKD with WCP is considered and further developed from two aspects.First, the security of the differential-quadrature-phase-shift (DQPS) protocol is proved.The DQPS protocol has essentially the same set up as the phase-encoding BB84 (PE-BB84) protocol, which is one of the most frequently demonstrated protocols.Since the known proof techniques for the BB84 protocol is not directly applicable, a modified approach is developed which is suitable for the DQPS protocol.As a result, the advantage of the DQPS protocol in the key generation rate over the PE-BB84 protocol is shown in the asymptotic limit where the size of communication data is assumed to be infinite.Second, a new method for security analysis with finite-key size is proposed as a suitable method for QKD protocols using WCP.Differently from the current method based on simple random sampling, the proposed method relies on Bernoulli sampling, which is associated with binomial distribution.The security of the BB84 protocol is proved by using the Bernoulli-sampling method, enabling a simpler analysis with a smaller number of parameters to be estimated compared to the method with simple random sampling.The required number of detected signals to generate a secret key is shown to be smaller than 10 4 , which is drastic improvement from the number ∼ 10 7 obtained in the previous result.The proposed method is also applied to the DQPS protocol, and its advantage over the PE-BB84 protocol is certified even in the finite-key regime.i
An essential step in quantum key distribution is the estimation of parameters related to the leaked amount of information, which is usually done by sampling of the communication data. When the data size is finite, the final key rate depends on how the estimation process handles statistical fluctuations. Many of the present security analyses are based on the method with simple random sampling, where hypergeometric distribution or its known bounds are used for the estimation. Here we propose a concise method based on Bernoulli sampling, which is related to binomial distribution. Our method is suitable for the Bennett-Brassard 1984 (BB84) protocol with weak coherent pulses [C. H. Bennett and G. Brassard, Proceedings of the IEEE Conference on Computers, Systems and Signal Processing (IEEE, New York, 1984), Vol. 175], reducing the number of estimated parameters to achieve a higher key generation rate compared to the method with simple random sampling. We also apply the method to prove the security of the differential-quadrature-phase-shift (DQPS) protocol in the finite-key regime. The result indicates that the advantage of the DQPS protocol over the phase-encoding BB84 protocol in terms of the key rate, which was previously confirmed in the asymptotic regime, persists in the finite-key regime.
One of the simplest methods for implementing quantum key distribution over fiber-optic communication is the Bennett-Brassard 1984 protocol with phase encoding (PE-BB84 protocol), in which the sender uses phase modulation over double pulses from a laser and the receiver uses a passive delayed interferometer. Using essentially the same setup and by regarding a train of many pulses as a single block, one can carry out the so-called differential-quadrature-phase-shift (DQPS) protocol, which is a variant of differential-phase-shift (DPS) protocols. Here we prove the security of the DQPS protocol based on an adaptation of proof techniques for the BB84 protocol, which inherits the advantages arising from the simplicity of the protocol, such as accommodating the use of threshold detectors and simple off-line calibration methods for the light source. We show that the secure key rate of the DQPS protocol in the proof is eight-thirds as high as the rate of the PE-BB84 protocol.
Abstract Quantum key distribution (QKD) is a secure communication method that relies on the inherent randomness of quantum mechanics to ensure information-theoretic security. The first and most widely used QKD protocol is BB84, and the proof of BB84's security is vital. The Discrete Phase Randomized BB84 protocol is a variant of the decoy BB84 protocol. It has been proven to be promising in the development of high-speed QKD systems. However, it still lacks an analysis with a finite number of pulses. This paper presents a comprehensive security analysis of the discrete phase BB84 protocol, using two different methods under different conditions. The analysis involves simulations and optimizations to determine the optimal parameter settings. It is confirmed that for typical scenarios, if the number of discrete phases exceeds 30, one can calculate the key rate by assuming that a continuous phase randomization process was in operation. On the other hand, for a relatively smaller number of discrete values, we have developed a numerical method to calculate the key rate. We have confirmed that its performance is reduced but still acceptable with a finite number of pulses.
Quantum key distribution (QKD) allows two users to communicate with theoretically provable secrecy [1]. This is vitally important to secure the confidential data of governments, businesses and individuals. As the technology is adopted by a wider audience, a quantum network will become necessary for multi-party communication, as in the classical communication networks in use today. Unfortunately, a number of phase-encoded QKD protocols based on weak coherent pulses have been developed. Whilst the first protocol, proposed by Bennett and Brassard in 1984 (BB84), is still commonly used, other protocols such as differential phase shift [2] or coherent one way QKD [3] are also adopted. Each protocol has its benefits; however all would require a different transmitter and receiver, increasing the complexity and cost of quantum networks. In this work we demonstrate a multi-protocol transmitter [4-6] that also has the benefits of small footprint, low power consumption and low complexity. We use this transmitter to give the first experimental demonstration of an improved version of the BB84 protocol, known as the differential quadrature phase shift protocol. We have achieved megabit per second secure key rates at short distances, and have shown secure key rates that are, on average, 2.71 times higher than the standard BB84 protocol. This enhanced performance over such a commonly adopted protocol, at no expense to experimental complexity, could lead to a widespread migration to the new protocol. The security of the BB84 protocol relies on each signal and reference pulse pair being globally phase randomised with respect to all other pulse pairs. In the DQPS protocol, blocks with a length L ≥ 2 are used and each block has a globally random phase with respect to all other blocks. Implementing this protocol would ordinarily require a high-speed random number generator and a phase modulator. As well as increasing device complexity, it would also require an unrealistic continuous source of electrical modulation signals for complete security. The transmitter we use injects light from a master laser diode into a 2 GHz gain-switched slave laser diode. The principal of optical injection locking means that the slave laser inherits the phase of the master laser. We apply modulations to the master laser current within a block to control the phase of the slave laser output pulses, and then drive the master laser below threshold for a short period of time when phase randomisation is required. This ensures the lasing comes from below threshold, thus the phase adopted by the slave laser pulse is completely random. We perform an autocorrelation measurement on the blocks to show their randomness. [1] N. Gisin et al. Rev. Mod. Phys. 74, 145 (2002). [2] K. Inoue et al. Phys. Rev. Lett. 89, 037902 (2002). [3] D. Stucki et al. Appl. Phys. Lett. 87 194108 (2005). [4] Z. Yuan et al. Phys. Rev. X. 6, 031044 (2016). [5] G. L. Roberts et al. Laser Phot. Rev. 11, 1700067 (2017). [6] G. L. Roberts et al. arXiv:1709.04214 [quant-ph] (2017).
Differential-phase-shift (DPS) quantum key distribution (QKD) is one of the major QKD protocols that can be implemented with a simple setup using a laser source and a passive detection unit. Recently, an information-theoretic security proof of this protocol was established by Mizutani et al. [npj Quantum Inf. 5, 87 (2019)], assuming an infinitely large number of emitted pulses. To implement the DPS protocol in a real-life world, it is indispensable to analyze the security with the finite number of emitted pulses. The extension of the security proof to the finite-size regime requires the accommodation of the statistical fluctuations to determine the amount of privacy amplification. In doing so, Azuma's inequality is often employed, but unfortunately we show that in the case of the DPS protocol, this results in a substantially low key rate. This low key rate is due to a loose estimation of the sum of probabilities regarding three-photon emission whose probability of occurrence is very small. The main contribution of our work is to show that this obstacle can be overcome by exploiting the recently found novel concentration inequality, Kato's inequality. As a result, the key rate of the DPS protocol is drastically improved. For instance, assuming typical experimental parameters, a 3-Mbit secret key can be generated over 77 km for 8.3 hours, which shows the feasibility of DPS QKD under a realistic setup.
Quantum Key Distribution (QKD) is one of the most promising technologies that enable theoretically unbreakable secure communications in this highly advanced information security era. This work provides a comparative analysis of QKD protocols such as BB84, Coherent One-Way (COW), and Differential Phase-Shift (DPS) against eavesdropping attacks e.g., Photon Number Splitting (PNS) attack. It employs a realistic approach to simulations such as using weak coherent pulse (WCP) sources. This work also explores qubit generation and the whole key distribution process in non-ideal conditions. Detailed algorithms have been discussed that simulate the encoding, transmission, and decoding process for every protocol, as well as simulating PNS attacks where an eavesdropper removes photons to gain key information without any detectable errors. Statistical metrics, such as Visibility and the information gain, are used to quantify the impact of these attacks. Future work aspects may include the extension of the simulation to incorporate additional parameters such as channel noise, fiber attenuation, detector dark counts, etc. to provide a realistic analysis to compare various QKD protocols.